Equality relations as a basis for fuzzy control
Fuzzy Sets and Systems
Why triangular membership functions?
Fuzzy Sets and Systems
The functional equations of Frank and Alsina for uninorms and nullnorms
Fuzzy Sets and Systems
Fuzzy equalization in the construction of fuzzy sets
Fuzzy Sets and Systems
On (un)suitable fuzzy relations to model approximate equality
Fuzzy Sets and Systems - Theme: Basic notions
A note on approximate equality versus the Poincaré paradox
Fuzzy Sets and Systems - Theme: Basic notions
On the relationship between T-transitivity and approximate equality
Fuzzy Sets and Systems - Theme: Basic notions
Fuzzy Sets and Systems - Theme: Basic notions
Fuzzy Sets and Systems - Theme: Basic notions
Why fuzzy T-equivalence relations do not resolve the Poincaré paradox, and related issues
Fuzzy Sets and Systems - Theme: Basic notions
Information Sciences: an International Journal
I-Fuzzy equivalence relations and I-fuzzy partitions
Information Sciences: an International Journal
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In this paper, we propose a practical method, given a strict triangular norm with a convex additive generator, for deriving a fuzzy equivalence relation whose reflexivity condition generalizes Ruspini's definition of fuzzy partitions. The properties of the relations, their comparison, their transitivity, the construction of fuzzy equivalence relations on cartesian products are presented. A large part of the paper is devoted to applications with fuzzy partitions defined on the real line. Several examples, including the fairy-tale problem from De Cock and Kerre [On (un)suitable fuzzy relations to model approximate equality, Fuzzy Sets and Systems 133 (2) (2003) 137-153], the comparison of colored objects and comfort situations are proposed.